Question

A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. How much time will A take to complete the remaining work alone?

Answer 1

Hint: In this problem, first we will calculate the work done by A and B per day and after that we will calculate the work done by B in 5 days and then only we can calculate the amount of time A requires to complete the remaining work.

Complete step-by-step answer:
 Here, we are given that:
The no. of days in which A can do a piece of work: 15 days
$\therefore $ The amount of work done by A in 1 day will be: $\dfrac{1}{{15}}$
The no. of days in which B can do a piece of work: 10 days
$\therefore $ The amount of work done by B in 1 day will be: $\dfrac{1}{{10}}$
Also, B works for 5 days only on the given work.
$\therefore $ the amount of work that B completed in 5 days will be= $5 \times \dfrac{1}{{10}} = \dfrac{5}{{10}} = \dfrac{1}{2}$
This implies that B completed half of the total work in his 5 days of work $\left( {\because 1 - \dfrac{1}{2} = \dfrac{1}{2}} \right)$
Therefore, the amount of the work after B, left for A will be $\dfrac{1}{2}$of the total work.
$ \Rightarrow $ The amount of time required for A to finish the work will be: $15 \times \dfrac{1}{2} = 7.5$
Hence, A can finish the remaining(half) piece of work in 7.5 days.

Note: In such problems, students might get confused because of the language of the question. So, it would be advisable to draw a schematic diagram step by step as the question proceeds in your head or rough space to sketch relations.
The time and work questions aren’t tough but tricky with the words. So, it is better for you to understand the language and write whatever is given on the firsthand to avoid confusion.